Performance expectancy: crystal ball for success

June 27, 2006 08:15 AM

Traders trade price and keep score by the bottom line. Account equity is their measure of success. Still, there is much more to be learned from the equity curve. As the well known trader Larry Williams has opined, “Traders have two tasks: first to trade the market and more important to trade their equity curve. That is the only way one can sidestep most of the dangers of trading.” What the equity curve reveals can vastly improve your bottom line.

Any serious discussion on equity is ultimately about defense. Data contained in the equity curve reveal clues as to whether the trading system will continue to perform as it has in the past. The trading record offers early warning to curtail losses and gives timely alerts to upcoming gains in the trading cycle.


Every series of market trades is part of a cycle where predictability is found in the frequency of wins and the size of wins relative to losses. A lot can be learned by monitoring their equity more closely. Although the trader’s primary affirmation is the bottom line, we can always use confirmation that our trades are still on the right track. Knowing the probable equity cycle for the next series of trades from a completely unbiased source, such as trading history, is more than just useful information. The predictive trends of equity-metrics give the assurance a trader needs to retain confidence that the trading system is still working.

All of the factors influencing market price are reduced by the trading methodology and delivered into the equity curve through the number and size of trading wins. It is the winning frequency and size of trades that drives the equity curve. Considering that a trend change in the equity curve is always preceded by a change in the drivers (winning frequency and size of wins), it is easy to understand the importance of monitoring these drivers for equity predictability.

Performance expectancy requires interpretation skills, which are acquired through observation of graphic representations of equity metrics to discover patterns that result in change. These patterns, while subtle, are recognizable and can be reduced to algorithms.

The important metrics for this introduction to performance expectancy are called “breakeven” for the breakeven point corresponding with the frequency of wins, and “expectancy” for the expectation of future gains. The way these metrics setup can be charted and used to predict future performance.


Performance expectancy is not about market price but rather about the outcome of the trading system in a particular market. The interpretation process is analogous to hitting a baseball.

The batter, knowing the strike count and game situation has an idea of what to expect. Now, picture this in slow motion. Beginning with the pitcher’s windup, release of the ball, its trajectory, spin and velocity, the batter recognizes that the ball is going to cross the plate in his favorite hitting zone. Crack! The batter hits the ball. Home run! As in the batting scenario, the expectancy and breakeven metrics give the trader progressive and recognizable clues in patterns that foretell the immediate and future success of the trading system.

Performance expectancy takes only three steps: 1) determine the trading profit picture throughout a reasonable period; 2) plot the profit record to reveal the nature of the winning cycles; 3) chart the performance expectancy metrics to reveal the probability of what will happen next.

Plotting the winning-ratio (average gain over the average loss) to weigh against the breakeven line for the trading history gives a visual indication of profitability and cycle tendencies. Using a moving average for a series of winning- ratio data points reduces system noise. For a trading system that is an overall winner, the majority of winning ratio plots will be above the breakeven line. The data points for the best wining trading systems will be clustered far above the breakeven line.

“Gold mining” (below) is a scatter plot of the winning-ratio moving average positions for 200 gold futures trades for a simple momentum trading system measured against the breakeven line. The winning-ratio of 1.36 is the overall average for all trades to be found above the breakeven line at 52% frequency of wins. The system-market combination is a winner, but not a barn-burner. The cluster of winning-ratios is wide ranging with some below the breakeven line.

Each position in “Gold mining” (below) is based on a 50-trade moving average. This reduces noise for a clearer look at longer-term trends. The bottom chart shows the same data based on a 20-trade moving average. This gives us a closer look at what has happened in the most recent gold futures trades. The last trade moving average is at 1.94 winning- ratio and 50% frequency of wins.

A tight cluster of winning-ratio plots is characteristic of low cycle tendencies. This adjusts as the length of the moving average for the winning-ratio is altered. The comparison of all the winning-ratio data points to the breakeven line may be varied from a single data point (the average winning ratio) to a few data points for the most recent trades.

To understand how changes in the breakeven points are related to changes in equity, the breakeven points are plotted as a curve in a time series chart.

A chart showing the equity curve with the breakeven curve reveals the trading system’s cycle tendencies. The breakeven metric is constructed from the average frequency-of-losses divided by the average frequency-of-wins. Once again, the presentation of the breakeven data points must be smoothed by resorting to the moving average plot. When the breakeven curve is below 1.00, equity builds up, and when above 1.00, equity decreases.

The degree of sensitivity for interpretation of the breakeven curve is governed by the length of the moving average. The moving average needs to be as short as possible for sensitivity yet long enough to discern its trend.


A downtrend in the breakeven curve, especially from above 1.00 crossing through 1.00, signifies equity building up, and the opposite is true for equity when the breakeven trend is rising, particularly when the breakeven curve is crossing up through 1.00. The chart of the equity curve with the breakeven curve reveals the nature of the unique cycle tendencies for prognostications about the specific trading system applied to the particular market under study.

“Tracking profitability” (below) is a chart of the equity curve (green line) displaying spurts of growth from near $5,000 to $15,000, then again from $15,000 to above $25,000. The breakeven curve crosses down through 1.00, then up through 1.00 only to cross down again. As the breakeven curve descends from its high at 1.40, equity begins to turn positive and remains positive until breakeven reverses to cross 1.00 on an upward slope.

The slope of the breakeven curve corresponds to the opposite slope in the equity curve. When breakeven crosses 1.00 from a distance, as here, its momentum signals a strong move in equity, and the projected trend of the breakeven curve, degree of slope and direction, presages and confirms the direction and strength of the following move in equity.

The trend and position of the breakeven curve by itself is useful for developing confidence in a trading system in the face of random trades that discredit the system. As long as the breakeven curve is below 1.00 and not rising on a positive slope, the trading system is quite safe to trade. As a single indicator the breakeven curve is not the only, nor the best, metric to follow.


Whereas the breakeven metric is constructed from the frequency of wins and losses, the expectancy metric is constructed from both the size and frequency of wins and losses. Expectancy is the average win multiplied by the frequency- of-wins divided by the average loss multiplied by the-frequency-of-losses.

A rising expectancy, especially through 1.00, signifies equity building. Relative confidence in this metric for predicting equity growth is resolved by the distance above 1.00, plus the trend and slope away from or toward 1.00. To facilitate the interpretation of both sensitivity and trend, expectancy can be plotted for a brace of short and long moving averages.

“What to expect” (below) shows the same gold futures trades shown earlier. Here, we show how the equity flat period is preceded by the decline in expectancy (blue line) and the crossing of breakeven up through 1.00. Then the buildup in equity is presaged by the decline of breakeven through 1.00 and the rise of expectancy above 1.00, both initially on steep slopes. Had expectancy dipped down sharply through 1.00 with breakeven above 1.00, the move would have been reflected by a significant decline in equity.

While probability is not certitude, for trading systems that have proven profitable performance expectancy is the first defense against a decline in performance as well as an excellent early alert to periods of exceptional buildup in equity. Before entering a position it pays to run a performance expectancy study.


The predictive quality of equity metrics applies to long-term investors as well as traders.

“Seismic shifts” (below) is a weekly chart of a trend following system for the investment in General Electric (GE) stock, showing how the crossing of expectancy and breakeven in the vicinity of 1.00 foretells the long equity rally that follows. Then the metrics recross near 1.00 — confirming the regression foretold in the daily charts — presaging the deep decline that follows the warning given by converging weekly metrics.

The decline ends with the metrics reversing to converge on 1.00 again, crossing 1.00 and each other ahead of another big rally. From this chart, it is easy to see how equity metrics are a useful stock picking and investment timing tool for investors.


Some system-markets combinations may be too erratic to trade — performance expectancy will reveal which ones. Extensive curve smoothing can delay the signals too much to be timely, causing a late swing.

When the moving average plots give conflicting signals, caution is required to select the right short-term or long-term trades based on the characteristics of the historic equity metrics.

The equity metrics are monitoring the outcome of a specific trading system operating on price movements in a particular market, which is not necessarily a price predictor. Nothing traders use now is replaced by performance expectancy. What equity metrics provide is additional information.

Prior to this close examination of equity, the insights afforded by equity metrics were perhaps only attainable through subconscious pattern recognition, otherwise known as trader’s intuition. Now, regardless of experience, every trader may add performance expectancy to their toolbox for finding the really good system-market combinations and for aborting markets before the trading system loses ground.

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